First, either use LaTex or use parentheses!
f(x)= (x-1)/(x-2), f(3)= 2 so you have
[(x-1)/(x-2)- 2]/(x- 3)

For the numerator, we have f(x)- f(3)= (x-1)/(x-2)- 2(x-2)/(x-2)= (x-1- (2x-4))/(x-2)= (-x+3)/(x-2) so the entire difference quotient is
(f(x)-f(3))/(x- 3)= (-x+3)/((x-2)(x-3))= -1/(x-2) because -x+3= -(x-3) and, for x not equal to 3, the x-3 terms cancel